The Russian barrage targeted five Ukrainian cities with more than 40 missiles of different types, hitting apartment buildings and public infrastructure, Ukrainian President Volodymyr Zelenskyy said in a social media post.
Strikes in Kryvyi Rih, in central Ukraine, killed 10 people and injured 37, in what the head of city administration, Oleksandr Vilkul, said was a massive missile attack.
At the Okhmatdyt children's hospital in Kyiv, rescuers were searching for people under the rubble of a partially collapsed wing of the facility.
Kyiv Mayor Vitali Klitschko said at least 16 people, seven of them children, were injured.
"It is very important that the world should not be silent about it now and that everyone should see what Russia is and what it is doing," he said, on social media.
Vsevolod Dorofieiev, the senior instructor of a volunteer medical unit, said some people had died but he did not say how many or whether they were children or adults.
The attack comes on the eve of a three-day NATO summit in Washington, which will look at how to reassure Ukraine of the alliance's unwavering support and offer Ukrainians hope that their country can come through Europe's biggest conflict since World War II.
At the children's hospital, a two-storey building was partly destroyed. On the hospital's main 10-storey building, windows and doors were blown out and walls were blackened. Blood spattered the floor in one room.
The intensive care unit, operating theatres and oncology departments were all damaged, officials said.
Medical personnel and local people searched for children and medical workers. Volunteers formed a line, passing bricks and other debris to each other.
Smoke still rose from the building, and volunteers and emergency crews worked in protective masks.
The attack forced the hospital to shut down and evacuate. Some mothers carried their children away on their backs. Others waited in the courtyard with their children as calls to doctors' phones rang unanswered.
A few hours after the initial strike, another air raid siren sent many mothers with their children hurrying to the hospital's shelter.
Led by a flashlight through the shelter's dark corridors, mothers carried their bandaged children in their arms and medics carried them on gurneys. Volunteers handed out candy in an effort to calm the children.
Marina Ploskonos' 4-year-old son had surgery for cervical spine tuberculosis last Friday.
"My child is terrified," she said.
"This shouldn't be happening, it's a children's hospital," she said, bursting into tears.
Ukraine's Security Service said it found wreckage from a Russian Kh-101 cruise missile at the site and had opened criminal proceedings on war crime charges.
The Kh-101 is an air-launched missile that flies low to avoid detection by radar systems. Ukraine said it shot down 11 of 13 Kh-101 missiles launched by Russia on Monday.
Hospitals and other medical facilities are protected from military strikes under international law unless they are being used for military operations.
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The International Criminal Court's founding charter says it is a war crime to intentionally attack buildings "dedicated to religion, education, art, science or charitable purposes, historic monuments, hospitals and places where the sick and wounded are collected, provided they are not military objectives".
Late last month, the court issued arrest warrants for Russia's former defense minister and its military chief of staff for attacking Ukraine's electricity network.
Czech President Petr Pavel said the hospital attack was "inexcusable" and that he expected at the NATO summit to see a consensus that Russia was "the biggest threat for which we must be thoroughly prepared".
Russia's Defence Ministry said the strikes targeted Ukrainian defense plants and military air bases and were successful.
It denied aiming at any civilian facilities and claimed without offering evidence that pictures from Kyiv indicated the damage was caused by a Ukrainian air defense missile.
Since early in the war that is stretching into its third year, Russian officials have regularly claimed that Moscow's forces never attack civilian infrastructure in Ukraine, despite what officials in Kyiv say and Associated Press reporting on the ground.
Elsewhere in Kyiv, the heaviest Russian bombardment of the capital in almost four months killed seven people and injured 25, officials said.
About three hours after the first strikes, more missiles hit Kyiv and partially destroyed a private medical center. Four people were killed there, Ukraine's Emergency Service said.
The daylight attacks included Kinzhal hypersonic missiles, one of the most advanced Russian weapons, the Ukrainian air force said. The Kinzhal flies at 10 times the speed of sound, making it hard to intercept.
City buildings shook from the blasts. An entire section of a residential multi-storey building in one district of Kyiv was destroyed, officials said. Three electricity substations were damaged or completely destroyed in two districts of Kyiv, energy company DTEK said.
The head of Ukraine's presidential office, Andrii Yermak, said the attack occurred at a time when many people were in the city's streets.
Klitschko said official assessments of the attack's consequences were still being carried out.
